As the question stands, it feels like it is not so much a question about philosophy, even though at the root of the question I believe you are asking about solipsism. I suggest you try to rephrase the question so that it is more evident that it is a question about a philosophical topic. That being said, see iep.utm.edu/solipsis/#H7 solipsism is a self defeating theory in many of the same ways that radical skepticism is.
– Not_HereApr 16 '17 at 9:38

Why would I try to convince you? I'll just wait until you die and go on with my life. You believe that I stop to exist when you die, so I really couldn't possibly care less about you.
– gnasher729Apr 16 '17 at 11:27

If the world does not exist after your death then there is no 'after'. The word 'after' implies the continuation of the world.
– PeterJApr 16 '17 at 12:44

define "this world", what is it, what does it amount to? are there other people in it? why would those other people cease to exist without you around? what about rocks, or busons? will you have a corpse, everyone else seems to?
– user25714Apr 16 '17 at 13:02

4 Answers
4

You can imagine the point of view of one of these other people, through being physiologically very similar to yourself.

The world exists now because you are in it and can observe it.

Similarly, you can imagine a different person being a main character, thus having the world exist without your existence.

Another point of view could be that being born and death are events contained within the world, and so is any idea involving the concept of time. The world cannot stop existing, or disappear because these are verbs relating to time, and only make sense within the world itself. If you think of the universe from a point of view outside the universe (so that time and space are just properties of this abstract object), you must conclude that as a whole it doesn't change in any way. Therefore whatever property you ascribe to it, such as existence, it either has this property or it doesn't.

If this sounds too alien, just consider that the universe could well be a mathematically definable construct similar to let's say - the Fibonacci sequence, or fractals or cellular automata. You wouldn't say that the sequence ever changes as a whole, although it contains a rule-based progression, and when following these sequences you might notice patterns come and go.

Neither of these explanations are of course complete, because existence can be defined subjectively, so that the word isn't meaningful without also specifying a subject. And if that subject is you - whose lifespan is only a tiny blip inside the universe, we must conclude that the universe's existence is also a tiny blip within itself. Or we might conclude that indeed the idea of existence doesn't apply to whole worlds, only specific things inside worlds.

How about considering the converse (or would it be "inverse"?) question, how to convince you that this world already existed even before you were born. If it didn't already exist, how'd you get here?

So, this answer to your converse question seems pretty compelling. But we'd ideally now like to interpret the converse of this answer as the hopefully-equally-compelling answer to your original question. But what's that converse answer??? Seems to sound something like, if the world doesn't still exist after you die, how can you be dead? That is, "nothingness" can't contain any dead people (or even the idea of once-alive-but-now-dead people). And this doesn't sound quite so compelling. Maybe you can work on it.

I'll start by saying that I can't prove it to you. For all you know, your experience constitutes the entirety of existence. That's not inconceivable.

All you can really do is use inductive reasoning. For one thing, you know that you have reactions to external stimuli, and those reactions are driven by your experience. For example, when you are hit, you experience pain. And when you experience pain, you express it in certain ways. Others follow a similar pattern. External stimuli that would cause you pain, when imposed on others, cause them to express themselves in a similar manner as you would. The only thing missing from your perspective is their pain. However, you know that, for yourself, that pain is a necessary link in the causal chain from the external stimuli to the pained reaction. So you might infer that pain is part of the process for them too, even though you can't observe it.

In science we often deduce things that are hidden from our senses when they're the best explanation for something. For example, the concentrated positive charge and dispersed negative charge of an atom was the best explanation for many experiment results, such as the Rutherford scattering experiment. So we deduced the structure of an atom without being able to see it directly. We simply accept it as the best explanation for the structure, until a better explanation comes along.

Others' reactions to painful stimuli, and its consistency with your experience is one of many methods in which you can infer that something you don't observe - the others' pain - is present. There are other examples. You know, for one thing, that if a concept you're unfamiliar with is introduced to you and after a short time you make an inference that couldn't be made without understanding of said concept, then you necessarily had the conscious experience of deliberating on this concept. So if you introduce a concept to another individual, and after a short time, they make an inference that requires understanding of said concept, you might infer that the necessary step of conscious deliberation was involved. It's not necessarily the case, but it is another hint that others have a conscious experience.

If things like this doesn't convince you that there are other conscious experiences besides your own, there are still other ways that there is still existence beyond your own experience. For example, as far as you're aware, humans can only come into existence through the birthing process performed by other humans, before that human is born. You are human, and you know that you didn't have conscious experience before you were born. Inductive reasoning would lead you to conclude that you likely came into existence by a process performed before you were born, which implies that events happened independent of your conscious experience. However, this is still inductive reasoning; it's possible that you're the sole exception to this rule, despite what your parents tell you. Similarly, you observe that existence carries on when others die, so you might infer that the same would be the case for yourself. Again, though, you might be the sole exception.

There's plenty of other ways you can infer that existence occurs independently of your experience, but only through inductive reasoning. Again, existence outside your experience is a phenomenon you don't observe, and, as with scientific phenomena, we can only infer things about the world that we don't observe through inductive reasoning. But we cannot disprove solipsism, so you have to live knowing that it is a possibility, however remote.

You are, of course, merely presenting your view of things. A child can do as much. And as little. Philosophy is not a solicitation to agreement with perspective, world-view, a way of looking at things, points of view or weltanschauung. Philosophy is love of wisdom and so requires knowledge, not opinion, sentiment or belief.

I think this world is like a movie only about me as the main actor.

That's nice. You are free to imagine whatever you are able, however, consider that often times the mind believes it is thinking while merely passing from one metaphor to the next.

How to convince me that I am wrong in this?

Philosophy does not contend with right or wrong, try instead: rationally assessing a truth value of exclusively either true or false.

Given your use of "this world" is true to you, it is worth pointing out the difference between what is true and what is true to you. Truth is merely a condition of statements and this condition is satisfied when what is said to be the case matches (corresponds to, fits) the case. Perspectival and situational statements of what is true to [you; me; us, or them] are not so constrained and need merely present a coherent framing. For example, it may be true to you that Van Gogh is a better painter than Picasso, yet if it is true to you that Van Gogh is still painting his landscapes upon the Venice boardwalk, then what is true to you (your belief) is simply false.

It means that this world will disappear right after my death.

In the metaphorical sense of "this world" as you are using it, sure, "your" "world" (everything that you experience and understand) will end when you die. In the empirically verifiable sense of the world - meaning everything that is - when you die, the world will continue without you. This happens every day, in fact, each time someone dies and the rest of us are still here to observe that we still exist.

How to convince me that this world still exists even after my death?

It is not the task of philosophy to convince you. Philosophy (read: respect for obtaining knowledge) is actionable and heuristic. I suggest if you have not that you take a logic class and study physics to ground your philosophical inquiries such that knowledge may be obtained. If you insist upon a solipsistic viewpoint that nothing exists except you, there simply is no refuting your insistence in much the same way that there is no countering a two-year olds "no!" Consider, however, that my solipsism is immediately refuted to you by you, and, your solipsism is immediately refuted to me by me. Consider also that we have a language which neither of us invented and that here we are communicating over the internet.